1. Technical Field
This application describes methods and apparatus for generating multi-dimensional maps of the spatial distribution of radio frequency (RF) magnetic fields (typically labeled as the “B1” field) in MRI (magnetic resonance imaging) systems.
2. Related Art
Magnetic resonance imaging (MRI) systems are by now well known and many different types of commercially available MRI systems are regularly employed for medical research and/or diagnostic purposes. Although there are many variations in detailed image acquisition processes and/or MRI system geometries, they all share some basic fundamental principles.
For example, MRI systems all utilize the principle of nuclear magnetic resonance (NMR) wherein nuclei having a net magnetic moment (e.g., nuclei having an odd number of protons such as the hydrogen nucleus) are immersed in a static background magnetic field B0. Ideally, this background static magnetic field is homogeneous throughout a volume to be imaged (even in the presence of the intervening object to be imaged). This background magnetic field tends to align a significant number of the nuclei magnetic moments therewith so as to produce a rather significant net nuclei magnetization aligned with the homogeneous background magnetic field B0.
The nuclear magnetic moments can be thought of as rotating about an axis at a frequency which is proportional to the magnetic field imposed upon the nucleus at its particular spatial location. The so-called Larmor angular frequency ω=γβ where γ is a gyromagnetic ratio constant for a given species of nuclei and its structural environment and β is the strength of the imposed magnetic field. Accordingly, in an ideal world, a particular species of nuclei having common physical surroundings would all have a common Larmor frequency of rotation. However, by superimposing an auxiliary magnetic field having a linear gradient (e.g., in one of three orthogonal directions x, y, z), it will be appreciated that the Larmor frequency of such common species of nuclei disposed along the changing field gradient will now have different values in accordance with the magnitude of the linear magnetic gradient field at the spatial location of a given nucleus. Again, in an ideal world, such superimposed magnetic gradient field would have only an exactly linear gradient in one desired dimension and otherwise be uniform and homogeneous. Typically, an MRI system has three sets of gradient coils arranged to impose linear magnetic gradient fields in each of three different mutually orthogonal directions.
By transmitting an RF magnetic field at the Larmor frequency into the volume that is to be imaged, one can selectively “excite” the nuclear magnetic resonant (NMR) nuclei that happen to fall within a given selected volume (e.g., a “slice”) so as to nutate the nuclear magnetic moment away from the nominal static magnetic field B0. Depending upon the amplitude and duration of such an exciting RF pulse, the magnetic moment of a nucleus can be “nutated” away from the nominal B0 alignment by controlled amounts (e.g., 90°). After such nutation, the nuclear magnetic moment tends to relax back toward nominal alignment with B0, but with characteristic longitudinal and transverse time constants T1, T2 and, in the process, each relaxing nuclear magnetic moment emits a radio frequency response signal that can be detected as an RF signal having a particular amplitude, frequency and phase (e.g., relative to the exciting RF field and/or to other NMR nuclei emitting RF response signals).
By carefully choosing a particular “MRI sequence” of RF excitation pulse(s) and magnetic gradient pulses, one can elicit meaningful spatially-encoded RF response signals so as to permit construction of an image or map of the NMR nuclei densities throughout a specific volume of the MRI system (e.g., a slice of the “imaging volume”). Over the last several decades of MRI system development, a very large number of MRI sequences have been discovered and commercialized. Since most, if not all, such imaging sequences can be utilized in the following exemplary embodiments, and since such are already well known to those skilled in the art, further detail about specific MRI sequences is not required.
The RF excitation fields transmitted into the imaging volume as well as the RF response fields received from the imaging volume are transmitted and/or received via RF coils which act as RF antennae. Once again, there are many different RF coil geometries well known to those in the art. For example, there may be “head” coils, “surface” coils, “whole body” coils, “multi-coil arrays” and the like. All of these RF antennae/coil structures serve to transduce electromagnetic radio frequency waves to/from NMR nuclei in the imaging volume onto feed line(s) of the RF antennae/coils which are then connected appropriately to RF transmitter and/or receiver circuits (e.g., via a transmit/receive switch if the same coil structure is used to both transmit and receive), as will be apparent to those skilled in the art.
Once again, in a perfect world, the RF antennae/coil sensitivity throughout the volume to be imaged is desirably absolutely uniform and homogeneous at all points within the volume to be imaged.
Unfortunately, the ideals of absolutely uniform homogeneity, absolutely linear gradients, etc., desired for various magnetic/RF fields in the MRI system are not realized in practice. Accordingly, various “shimming” attempts are made to correct for unwanted departures from the ideal and/or to compensate acquired signals that have been adversely affected by such less than ideal circumstances.
This application is directed towards a new and improved technique for mapping of the RF B1 magnetic field associated with transmit sensitivity of the RF antennae/coils of an MRI system. Various prior techniques have been used for generating such B1 maps which are then used either to improve the design of the MRI system itself and/or to provide compensated output images from the MRI system (e.g., especially where quantitative measurements are to be made based upon such images). However, as will be explain below, such prior techniques leave room for improvement—which the exemplary embodiments explained in detail below provide.
Some examples of prior approaches that may be relevant to the present application are identified below:                1. L. Axel, L. Dougherty, “MR Imaging of Motion with Spatial Modulation of Magnetization,” Radiology, Vol. 171, pages 841-845 (1989)        2. L. Axel, L. Dougherty, “Heart Wall Motion: Improved Method of Spatial Modulation of Magnetization for MR Imaging,” Radiology, Vol. 172, pages 349-350 (1989)        3. E. K. Insko, L. Bolinger, “Mapping of the Radiofrequency Field,” J Magn Reson (A), Vol. 103, pages 82-85 (1993)        4. R. Stollberger, P. Wachs, “Imaging of the Active B1 Field in Vivo,” Magn Reson Med, Vol. 35, pages 246-251 (1996)        5. N. G. Dowell, P. S. Tofts, “Fast, Accurate, and Precise Mapping of the RF Field In Vivo Using the 180° Signal Null,” Magn Reson Med, Vol. 58, pages 622-630 (2007)        6. F. Jiru, U. Klose, “Fast 3D Radiofrequency Field Mapping Using Echo-Planar Imaging,” Magn Reson Med, Vol. 56, pages 1375-1379 (2006)        7. J. T. Vaughan, M. Garwood, C. M. Collins, W. Liu, L. DelBarre, G.        
Adriany, P. Anderson, H. Merkle, R. Goebel, M. B. Smith, K. Ugurbil, “7T vs. 4T: RF Power, Homogeneity, and Signal-to-Noise Comparison in Head Images,” Magn Reson Med, Vol. 46, pages 24-30 (2001)                8. J. Wang, W. Mao, M. Qiu, M. B. Smith, R. T. Constable, “Factors Influencing Flip Angle Mapping in MRI: RF Pulse Shape, Slice Select Gradients, Off-Resonance Excitation, and B0 Inhomogeneities,” Magn Reson Med, Vol. 56, pages 463-468 (2006)        9. V. L. Yarnykh, “Actual Flip Angle Imaging in the Pulses Steady State: A Method for Rapid Three-Dimensional Mapping of the Radiofrequency Field,” Magn Reson Med, Vol. 57, pages 192-200 (2007)        10. M. A. Bernstein, K. F. King, X. J. Zhou, Handbook of MRI Pulse Sequences, Elsevier Academic Press, especially pages 166-171 (2004)        11. X. Chen, X. Shou, W. R. Dannels, “Feasibility of Rapid B1 Mapping with RF Prepulse Tagging,” Proceedings of ISMRM, 16th Scientific Meeting, Toronto, Canada, May 2008 Abstract #3045        12. X. Chen, X. Shou, W. R. Dannels, “Feasibility of Rapid B1 Mapping with RF Prepulse Tagging,” poster presented at Research Showcase 2008, Case Western Reserve University, Veale Convocation Center, Cleveland, Ohio, Apr. 16-17, 2008.        
MRI requires both transmitted radio frequency (RF) fields and received radio frequency (RF) fields. These RF fields are often denoted as B1 fields. The transmitted field, in typical usages, should be approximately uniform over the area being imaged within the subject. Spatial inhomogeneities of the RF fields introduce unwanted effects, including various artifacts in images, degradations in image contrast, or degradation or failure of various quantification methods. The transmit field acting within human bodies exhibits greater non-uniformity as main magnet field strength increases. The static magnetic main field is denoted as the B0 field. The effective B1 fields depend both upon the engineering design of the MRI scanner (such as RF antenna/coil geometry), and the geometry and electromagnetic properties of the subject within the scanner (often a human patient).
Having information about the distribution of non-homogeneity in the transmit B1 field within a specific subject can be beneficial in various ways. Advantages of having such data include being able to better interpret images and artifacts, being able to spatially improve the actual field patterns by improved design of the scanner, being able to interactively or dynamically refine the fields on specific subjects and in specific scan areas, and being able to improve or correct the acquired data and/or resulting images. In some more advanced methods, such as “multichannel transmit” or “Transmit SENSE,” knowledge of non-uniform spatial field patterns is explicitly needed and explicitly used to accomplish goals of improved RF excitation and spatial localization.
Numerous methods exist or have been proposed for experimentally determining the B1 field. When the information is determined or presented in the form of a 2-D or 3-D spatial distribution, it is called a B1 map.
A pulse sequence can be repeated several times using successive amplitudes of RF excitation (i.e., nutation) pulses. The receive MR signal intensity is known to have a certain functional dependence on the effective B1 transmit amplitude, such as:S(θ(x,y,z), x,y,z)=[ρ(x,y,z)]*sin(θ(x,y,z))3   [Equation 1]θ(x,y,z)=RF_ampl_factor*(B1_spatial(x,y,z))   [Equation 2]where:                S is measured data (using a pulse sequence acquisition at the scanner for various RF_ampl_factor values), and the unknown value of B1_spatial (i.e., θ or B1_spatial) are the spatial distribution(s) to be determined;        “S” denotes the MR signal intensity (the actual mathematical functional dependence is based upon the pulse sequence used);        ρ is a signal strength factor such as the proton density, or a proton density times the receive coil sensitivity, or the like;        RF_ampl_factor is an independently adjusted control factor (e.g., RF pulse amplitude and duration) in the pulse sequence;        B1_spatial(x,y,z) is the form of a spatially dependent B1 associated with some reference value of the RF_ampl_factor; and        θ has the meaning of the spatially dependent effective B1 field.        
The specific “S” formulae given above happen to be suitable for a pulse sequence producing a single stimulated echo with complete T1/TR signal recovery, and minimal T1, T2 decay during the echo time, just as an example.
In general, one detects or measures S, from which one can determine θ, from which one can determine B1_spatial. In the literature, sometimes authors compute and report θ, and sometimes they compute and report B1. Converting from one to the other is simple, and the two terms may be used somewhat interchangeably throughout the following description.
To be rigorous, B1_spatial should represent an instantaneous physical measurement of a component of a time-varying magnetic field. θ is the time integral of (γB1), and γ is a gyromagnetic ratio. The time integral can be a simple linear approximation or, more accurately, it can be the result of integrating out the full Bloch equations. These relationships are well known in MRI, and are not discussed further here. Suffice it to say, conversion between B1 and θ is straight-forward under typical imaging conditions.
Multiple measurements are generally needed, so that from multiple values of S, it is possible to solve for “ρ” and θ.
Spatially localized images can be collected at a series of amplitudes. Analysis such as searching for a peak, or fitting a curve, can be done to determine the strength of B1. In a simple exemplary case, such as a stimulated echo sequence where S=S(θ)=sin(θ)3, if we assume an approximately uniform B1_spatial(x,y,z), MR data can be collected at each of several RF_ampl_factor values over some nominal range. The RF_ampl_factor which yields the peak of the signal value “S” corresponds to θ(x,y,z)=π/2 (flip angle in radians), i.e., at the particular RF_ampl_factor for which S achieves a maximum, B1_spatial=(π/2)/RF_ampl_factor (once again, ignoring other factors such as γ, the RF pulse duration, etc.).
Other pulse sequences can be used, and other features of the signal strength function can be used, such as the first minimum of the signal for a 180° excitation pulse sequence, or such as the most-negative-valued signal for a 180° inversion pulse followed by a sign-sensitive readout.
The successive amplitudes can be controlled by stepping through a range in a prescribed fashion, perhaps linear increments across some nominal range, or by iterative search methods like bisection, etc.
The varying amplitude factor, RF_ampl_factor, can be altered and applied to all RF transmit pulses in a sequence in unison or, alternately, one or a few pulses can be modified, while others are kept constant. For example, in a spin echo pulse sequence with two nutation pulses (α1 and α2), the signal strength can have the form:S(α1, α2)=sin(α1)*(sin(0.50 α2))2,in which case α1 and α2 may be varied together, or either one can be varied independently.
When B1_spatial(x,y,z) is not treated as constant (i.e., spatially homogeneous), a simple but slow technique is to acquire and generate entire 2-D or 3-D images for each of several RF gain factors, and then to analyze the sets of images pixel-by-pixel, to fit or search for an amplitude scaling at each pixel location. Note that while using search algorithms and data-dependent choice of RF_ampl_factor to try to converge to some optimal condition may be a good strategy when B1 is spatially uniform, it is not as suitable when B1 is non-uniform. A value of RF_ampl_factor which achieves a goal such as a signal null at one location will not simultaneously achieve nulls at other locations, for example.
The resulting B1 strengths, or flip angles θ, are then collected and presented or stored in the form of an image, known as a B1 map. It is possible that the B1 value can be treated either as a magnitude or as a complex value which also includes some phase value (relative to a suitable or arbitrary reference phase).
Many acquisition methods are known which can be used to determine B1. Basically, all MRI pulse sequences have dependencies on B1 transmit fields, but some have more favorable characteristics, such as nearly linear dependencies over a range of transmit values, or such as dependencies which are uncoupled from other variables like the tissue T1 and T2 parameters. Corresponding analysis methods also exist, often for specific acquisition methods.
In some cases, a series of many RF pulse amplitudes are used in successive acquisitions. A feature such as a null or minimum in the signal level can then indicate which RF pulse amplitude is the nearest match to a certain flip angle or a certain B1 strength, as previously explained.
Determining θ from S may be done in any of a few ways. There can be some regression or fitting to yield both ρ and S (even though there may be no explicit interest in ρ). There could be a simple search for a simple feature of the signal curve such as a maximum or null. There are ways to collect a few values of S, (perhaps something like S1 using RF_ampl_factor=RF_amp_factor1, and S2 using RF_ampl_factor=(2*RF_ampl_factor1), then finding a closed form mathematical dependence of θ on S1 and S2, especially where that closed-form dependence has eliminated other variables like ρ.
It is common to collect pairs of images acquired with different numbers of RF pulses, or different amplitudes, and then form ratios of the images. The ratios cancel other factors contributing to image intensity, leaving terms which depend on the RF pulses. The signal ratios have dependencies upon the RF pulse amplitudes which can be computed and inverted.
We have previously described collecting data with a few values of RF_ampl_factor, each using the same pulse sequence and the same acquisition parameters (other than RF_ampl_factor). A variant of this idea, is to acquire instead two (or more) pulse sequences, two or more echoes, or the like. In one example, the two basic pulse sequences could be different, and each has a different functional dependence of S on θ (e.g., one spin echo with a saturation or inversion pre-pulse, and a second spin echo without the pre-pulse). In another example, two or more echoes can be acquired in a single, more complicated, pulse sequence (e.g., a spin echo and a stimulated echo, or some kind of first RF echo and second RF echo). In yet another example, a pulse sequence can be run with two sets of parameters, such as a short TR and a long TR, perhaps in an interleaved fashion.
One commonly referenced method which is an example of such a ratio calculation is the double angle method. (Insko, 1993; Stollberger, 1996, etc.)
It is known that RF tagging techniques (including “SPAMM”) depend upon RF amplitudes, and so they can be used for determining B1 spatial dependencies (B1 maps). (Axel, 1989, two references.)
In SPAMM RF tagging, two or more similar RF tagging nutation pulses are applied, and a pulsed gradient is applied in between them. The gradient causes spatial “modulation patterns.” One simple pattern is a periodic set of parallel stripes, with each cycle showing a generally sinusoidal intensity pattern. A simple physical explanation is that the two RF pulses can have similar effects individually, but the gradient applied after the first pulse causes a spatially dependent phase factor associated with the first RF tagging pulse. Then, depending upon this phase factor, the two RF tagging pulses may “add constructively” or “cancel each other like a destructive interference.” Thus, a series of stripes is generated, with bright untagged signal appearing at locations where the tagging pulses cancel each other, and with tagged reduced (dark) signal bands appearing in locations where the effects of the two RF tagging pulses combine together constructively. A mathematical description of this is given in Bernstein, King and Zhao, pages 166-171, 2004.
Bernstein at page 176 has a cursory reference to the fact that SPAMM pre-pulses can be used to figure out B1 maps. There are also some similar cursory references in one or both of the original Axel papers. While such references say it can be done, the inventors are not aware of anyone really doing it or publishing results until they did a version at the ISMRM Toronto May 2008 conference—and that was with purely image-based processing. When considering prior art use of SPAMM to achieve B1 mapping, it appears that there is limited published material.
The Axel papers allude to the fact that spatial tagging lines may appear as pairs of minima under certain conditions, and that the spatial separation of the pair of minima could be used to determine B1. The conditions for favorable application of this acquisition method and analysis approach can include a total tagging excitation higher than 90° (perhaps between 110° and 270°), magnitude image reconstruction, and image pixel resolution of multiple pixels across each full spatial cycle of the complicated tagging pattern.
Suppose the two pulses each have some nominal amplitude at a particular location, each yielding (perhaps) 35° tip angle in some region. The tagging portion of the acquisition sequence can then be described as having a total tagging RF nutation angle of 70°, which dictates the percentage of signal suppression at a trough in that region.
The prior Dannels, Chen and Shou approach using SPAMM-tagging for the acquisition (but a different analysis concept from that now to be described below) prefers a different set of favorable acquisition conditions. When the total tagging RF angle is less than about 90°, then the relative darkness of tagged areas can be used directly to determine the tagging RF angle. The resultant image has a structure of alternating bands or stripes, with both tagged and untagged signal. Bright peaks are untagged, and the darkest part of each trough corresponds to a location which is affected by the total tagging RF pulse's total B1 angle. Under such conditions, the ratio of a peak to a trough can then be sufficient to determine the effective B1 field. With such a strategy, the peak and trough are acquired totally simultaneously, in a single image. Thus, there should be minimal concerns about the sources of inconsistencies which exist between two or more measurements. (Patient motion is the most notorious source of these inconsistencies.) This is an intrinsic advantage of using the tagged image. In exchange for getting away from the data-consistency problem of using two or more acquisitions, the tagging method will, however, depend upon other consistency concerns across two or more locations. For example, the signal strength ratio is attributed to an RF tagging pulse (difference between a peak and a trough) and its local B1 field, so there should not be other major sources of deviation in “S”, such as confounding differences due to “ρ” or T1 or T2.
In an abstract submitted in November 2007 to the ISMRM conference of May 2008, one of the inventors (plus co-authors Chen and Shou) presented analysis of a method of detecting nearby peaks and valleys in an image with tagging, to compute the effective RF pulse amplitude which created the tag. The inventors consider this to be not a particularly effective method. (See “Feasibility of Rapid B1 Mapping with RF Prepulse Tagging,” X. Chen, X. Shou, W. Dannels, Proceedings of ISMRM 16th Scientific Meeting, Toronto, Canada, May 2008 abstract #3045.) Also documenting this approach is a poster which analyzes use of the same tagging acquisition, but using the (image-domain) processing of peaks and valleys. This poster was presented at Case Western Reserve University in April 2008.
Many of such prior techniques for B1 mapping have limitations of acquisition speed. For example, one minute for a 2-D map, or four minutes for a 3-D volume map, have been touted as being “fast” B1 mapping techniques. Motion artifacts in the body can degrade individual images, but more importantly, they can cause inconsistencies between pairs of images. Inaccuracies and biases can arise. Effects from T1 decay have been often analyzed. Techniques may require additional corrections or calibration (e.g., double angle is known to have a confounding effect, where selective excitation slice thickness and profiles exhibit an undesired dependence upon the local B1). (See Wang, 2006.) Arrival of signal level to equilibrium or steady state values can be slow, e.g., on the order of a few times T1. This can limit scan time or limit temporal resolution, or introduce errors in the presence of attempted faster acquisitions. Intrinsic SNR can adversely affect accuracy, resolution or scan acquisition time. There can be a limited dynamic range with respect to the deviation of B1 relative to a known nominal value. (See, for example, Dowell, 2007.) The associated acquisition technique for reading out the image may have limitations or artifacts, which would propagate into the associated maps. For example, EPI, as used in Jiru, 2006, can have significant geometric distortion, or chemical shift, or utilizes fat suppression, making it impractical to determine the B1 within fat.
Most of the prior techniques require longer acquisitions, costing several minutes of scanning for 2-D or 3-D maps. In many of these techniques, the different acquired images depend on not only RF pulse amplitudes, but also other factors such as T1, T2, or resonance frequency shifts, etc. This becomes a source of error in the resulting B1 determination, or else requires additional acquisitions to simultaneously determine both B1 and the other factors. When scans are longer, or more than one scan must be combined, physiological motion can degrade the individual acquired images, or make the separate images become inconsistent, ruining the ratios. Motion artifact can make techniques useless in human torsos. Using single tagged images avoids these problems, but requires more sophisticated processing. Detection of local signal variations in a tagged image, when the unmodulated image itself contains significant local variation, is not easy, especially when working in the image domain.
If the SPAMM acquisition is used with image-domain peak-and trough detection method, significant error can arise if a neighboring peak and trough are used together in a ratio, but they have other confounding effects, like major differences in ρ.